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arXiv · 2311.11391

A study guide for "Trilinear smoothing inequalities and a variant of the triangular Hilbert transform"

Martin Hsu·Fred Yu-Hsiang Lin·Amelia Stokolosa
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Abstract

This article is a study guide for "Trilinear smoothing inequalities and a variant of the triangular Hilbert transform" by Christ, Durcik, and Roos. We first present the standard techniques in the study of oscillatory integrals with the simpler toy model of a Hilbert transform along a parabola. These standard techniques prove to be insufficient in the study of the triangular Hilbert transform with curvature. The central and novel idea in their proof of the $L^p$-boundedness of the triangular Hilbert transform with curvature is a trilinear smoothing inequality which we also examine in this article.

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Martin Hsu, Fred Yu-Hsiang Lin, Amelia Stokolosa. 2023-11-19. A study guide for "Trilinear smoothing inequalities and a variant of the triangular Hilbert transform". https://arxiv.org/abs/2311.11391

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